Q. 39 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35–42, graph each system of inequalities by hand 

$\left\{\begin{array}{l}{x}^2 + y^2 \le 16 \\ y\ge x^2 - 4\end{array}\right.$

Step-by-Step Solution

Answer

The graph of the system of inequalities is 

Step 1. Graph of the inequality x 2   +   y 2   ≤   16

The graph of the inequality $x^2+y^2\le 16$can be plotted by graphing

Since the point $(0, 0)$ satisfies the inequality,

therefore, it will be included in the shaded region.

Step 2. Graph of the inequality

The graph of the inequality $y\ge x^2-4$can be plotted by graphing

Since the point $(0,0)$ satisfies the inequality,

therefore, it will be included in the shaded region.

Step 3. Final graph

The intersection of both the graphs of the inequalities gives the final graph.